abstract algebra: prove that there is no simple group of order $ 216 = 2 ^ {3} cdot 3 ^ {3} $.

I feel like I'm supposed to use the index theorem here, but when I use Sylow's third theorem I have that $ n_ {3} in {1,4 } $. I'm not sure how to rule out the possibility that $ n_ {3} = 4 $. If you could, you could use the fact that the only Sylow 3 subgroup is normal in G to factor it out and apply the Index Theorem. Any suggestion?

complexity theory: validity of a simple polynomial time reduction

Let's say P is a NP-hard optimization problem and Q is a problem with unknown complexity. Also, we have an algorithm to solve problem Q. We can solve problem P with input x as follows:

    max = -inf - the optimal value for P 
    n = size of x
    for (i = 1; i <= n; i++)
         val = solveQ(x, i)
         if (val > max) max = val

Is this a proof that Q is also NP-hard? If so, can this be shown more formally? Is this a valid polynomial time reduction?

magento2 – Grouped Product Reviews – getting and displaying simple reviews of associated products

It's frustrating that the Magento core has a mechanism to handle configurable option reviews on a configurable product, but NOT simple products on bundled products.

My site uses grouped products. Since all orders are for simple products, reviews end up being simple products, but these will not show up on the grouped products page. I am looking to a) extend the review block to add simple product reviews and (ideally) b) extend the rating calculation to also include simple product ratings.

I've looked everywhere for any review extensions that support bundled products and couldn't find any. So I try to figure it out myself.

The first attempt has been to try to extend the MagentoReviewBlockProductViewListView Block to get the associated product ID list and to pass this list to the collection classes, then somehow I need the collection classes to search for a list of products instead of just one.

Collection classes MagentoReviewModelResourceModelReviewProductCollection Y MagentoReviewModelResourceModelReviewCollection build a query through method AddEntityFilter using the exact match this should be changed from entity_pk_value=? to entity_pk_value in (?).

This is a small change that is technically backward compatible, so I tried using a plugin first. Unfortunately, query building is all protected methods, so plugins can't work, or I got errors or got patches that just don't show.

It seems like I need to extend the collection classes as a whole just to make that change.

Is there a better way?

simple unit animation with images

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You need a simple website made

I am looking for a simple 3 page site. The first page is a voting page and the second is the results of one voting button and the third is the results of the other voting button. I would like it to be like a tip jar and look like "addthis". Com ”has just what I want.
Let me know if you can do this or should I continue with Fiverr?
Thank you.

algorithm – simple 2D city simulation

everyone. I want to create a small simulation of the city. Let me explain what I have and what I mean by that …

For starters, everything will be more abstract. So, my city is actually a set of rectangles: "houses" (fairly easy conflicts to handle) and a set of points: "towns". All this will be in 2d.

Since I have points (they will move, because residents also move around the city, right?) And rectangles, I decided to take the quadtree as a base.

quadtree city

So the general plan of what I would like to get.

  1. Points must walk through the city (obviously yes? but not like this
    easily) during such walks (and points – residents should not walk
    all in the same direction) the points would go to different rectangles
    (it seems that you are going to work or buy).
  2. Change of day and night. Suppose I have a stop button (after which
    all points stop – the city stops) and the start button (all
    points start walking) I wish each point had a home (sounds good, doesn't it?). Suppose the day lasts, for example, 30 seconds. At the beginning of this time, the point comes out of your house (rectangle), which was predetermined somewhere. Start walking around the city (see point 1 above) and at the end of the day, start walking home, back to your rectangle. ("House")

For simplicity, we will assume that all houses do not move and are defined in advance.

My main problem is that I don't know how to do paragraph 2.
I don't know how to do a "point tour" in the city. There can be many points (for example 5000) and having a good fps for each point the route would be problematic, perhaps it is worth doing "common routes", some lines around the rectangles that run through most points.

I have an idea of ​​how to make a point sometimes "go" to some rectangle. To make each rectangle have a radius and with a certain probability every second, each point will be forced to enter some rectangle (house).

Now a little bit about the code:

What we have is a standard quad tree, with standard methods (eg inserting points). The structures responsible for points and rectangles:

struct Point {
   x int;
   y int;

functions for Point {
   moveTo(x int, y int){
      p.x = x;
      p.y = y;
struct Rectangle {
   x int;
   y int;
   width int;
   height int;

All of our drawing field will be determined. For simplicity, make it a 1000×1000 pixel canvas.
And each point is just a separate pixel on it.

What else can we do? We can make "street" a space (series of pixels) between houses:


Waiting for your help and advice!

python: a simple animation in pygame

I am following a tutorial on pygame. I noticed that the sample code was written for the sake of being easy to understand. I was wondering if I could & # 39; improve & # 39; the code, focusing on keeping exactly the same functionality. I tried, but I'm not really sure if this is an improvement.

This is the original code of the instructions:

import pygame, sys
from pygame.locals import *


FPS = 30 # frames per second setting
fpsClock = pygame.time.Clock()

# set up the window
DISPLAYSURF = pygame.display.set_mode((400, 300), 0, 32)

WHITE = (255, 255, 255)
catImg = pygame.image.load('cat.png') # hosted at https://inventwithpython.com/cat.png
catx = 10
caty = 10
direction = 'right'

while True: # the main game loop

    if direction == 'right':
        catx += 5
        if catx == 280:
            direction = 'down'
    elif direction == 'down':
        caty += 5
        if caty == 220:
            direction = 'left'
    elif direction == 'left':
        catx -= 5
        if catx == 10:
            direction = 'up'
    elif direction == 'up':
        caty -= 5
        if caty == 10:
            direction = 'right'

    DISPLAYSURF.blit(catImg, (catx, caty))

    for event in pygame.event.get():
        if event.type == QUIT:


This is my & # 39; improved & # 39; code. Two questions. In general, how can my version be improved and why is that improvement better than my code? And how could the original be improved?

import pygame, sys
from pygame.locals import *


FPS = 30
fps_clock = pygame.time.Clock()

window_size = (400,300)
DISPLAYSURF = pygame.display.set_mode(window_size,0,32)
pygame.display.set_caption("Animation test!")

WHITE = (255,255,255)
cat = pygame.image.load('assests/cat.png') # hosted at https://inventwithpython.com/cat.png
direction = 'right'
x_,y_ = 10,10

def listenToQuit():
    for event in pygame.event.get():
        if event.type == QUIT:

def detectCollision(cat,x,y,window_size):
    return cat.get_size()(0) + x >= window_size(0) or 
        cat.get_size()(1) + y  >= window_size(1) or 
            x <= 0 or y <= 0

def getDirection(direction):
    directions = ('right','down','left','up')
    idx = directions.index(direction)
    idx = 0 if idx + 1 == len(directions) else idx + 1
    return directions(idx)

def getMovement(x,y,direction):
    if direction == 'right':
        return x+5,y
    elif direction == 'down':
        return x , y+5
    elif direction == 'left':
        return x - 5 , y
    elif direction == 'up':
        return x , y - 5

i = 0
while 1:

    x,y = getMovement(x_,y_,direction)
    while detectCollision(cat,x,y,window_size):  # if there would be a collision, change direction 
        direction = getDirection(direction)
        x,y = getMovement(x_,y_,direction) # re-calculate movement, now avoiding collision

    x_,y_ = x,y



I specifically chose not to make the animated object a class. I will try to do it as my next exercise towards myself.

Magento2.4 tries to import simple products through csv

I am trying to import products through a csv in Magento2.4, the file is a little big, it is 189 MB in size.
I edited the php.ini file to allow for a larger max_imput_size and larger upload_max_filesize. I restarted Apache, but now when I upload the file, a spinning arrow appears in the browser that never disappears.
I'm not sure what else I could do to keep this from getting stuck.


A simple question

Hi there,

I have just established my general trading company and want to start the wholesale and distribution business,

1: My question is if my company and other wholesale company want to invest or buy a stock of items together, then we sell it and divide the profit, what's this process called?

2: My second question of identification when buying or selling the shares we buy, who should be the one who does the invoices, if my company or the company with which I am investing together?

Thank you

javascript: simple old game without changing HTML

I'm working with JavaScript to make a tic tac toe game, but I can't change anything in the HTML.
I'm not going to pass a part, I wanted a red or blue square to be inserted where the user clicked, depending on the player's turn.

Here is the function I am doing.

    function inicializar(){
        var preenche = document.querySelectorAll("div")(2,3,4,6,7,8,10,11,12);
        for(var i=0; preenche

It is the HTML code that cannot be modified.